# How do you calculate Log_3 63?

Jul 16, 2016

$3.771$

#### Explanation:

Some calculators can work out logs with any base, but we can work it out without that function.

By definition If ${\log}_{a} b = c , \text{ then } {a}^{c} = b$

Let ${\log}_{3} 63 = x \text{ then } {3}^{x} = 63$

$\log {3}^{x} = \log 63$

$x \log 3 = \log 63$

$x = \frac{\log 63}{\log 3} = 3.771$

This is the same result we would get using the change of base law.

${\log}_{3} 63 = \frac{{\log}_{10} 63}{{\log}_{10} 3}$

$= 3.771$